Answer:
z = -5
Step-by-step explanation:
3(0.7z + 2.8) = 7(1.5z + 7.2)
2.1z + 8.4 = 10.5z + 50.4
2.1z - 10.5z = 50.4 - 8.4
-8.4z = 42
z = 42/(-8.4)
z = -5
can someone help me solve this problem
Answer:
18 and 40
Step-by-step explanation:
Let x be the age of Claire and y the age of her mother
Claire's mother is 4 years more than twice Claire's age
y = 2x+4The sum of their ages are is 58
x+y = 58the system is:
[tex]\left \{ {{y=2x-4} \atop {y+x=58}} \right.[/tex]
Multiply (y+x = 58) by -1 and then add it to (y = 2x+4) to eliminate y
-y-x = -58 -y-x+y = 2x+4-58 -x -2x = -54-3x = -54x = 54/3x = 18y= 58-18 = 40
so claire's mother is 40 years old and claire is 18
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables a. More than 61 pounds
Answer:
0.007
Step-by-step explanation:
We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage
Step 1
We would have to find the sample standard deviation.
We use the formula = σ/√n
σ = 12.2 pounds
n = number of house holds = 51
= 12.2/√51
Sample Standard deviation = 1.7083417025.
Step 2
We find the z score for when the sample mean is more than 61
z-score formula is z = (x-μ)/σ
where:
x = raw score = 61 pounds
μ = the population mean = 56.8 pounds
σ = the sample standard deviation = 1.7083417025
z = (x-μ)/σ
z = (61 - 56.8)/ 1.7083417025
z = 2.45852
Finding the Probability using the z score table
P(z = 2.45852) = 0.99302
P(x>61) = 1 - P(z = 2.45852) = 0.0069755
≈ 0.007
Therefore,the probability that the sample mean will be more than 61 pounds is 0.007
Suppose the sequence StartSet a Subscript n Baseline EndSet is defined by the recurrence relation a Subscript n plus 1equalsnegative 2na Subscript n, for nequals1, 2, 3,..., where a1equals5. Write out the first five terms of the sequence.
Answer:
-10, 40, -240, 1,920 and -19, 200
Step-by-step explanation:
Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.
when n= 1;
aₙ₊₁ = -2naₙ
a₁₊₁ = -2(1)a₁
a₂ = -2(1)(5)
a₂ = -10
when n = 2;
a₂₊₁ = -2(2)a₂
a₃ = -2(2)(-10)
a₃ = 40
when n = 3;
a₃₊₁ = -2(3)a₃
a₄ = -2(3)(40)
a₄ = -240
when n= 4;
a₄₊₁ = -2(4)a₄
a₅ = -2(4)(-240)
a₅ = 1,920
when n = 5;
a₅₊₁ = -2(5)a₅
a₆ = -2(5)(1920)
a₆ = -19,200
Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200
Which of the following is represented by MN?
Answer: MN represents the radius of the circle.
Step-by-step explanation:
The radius is the distance from the center to the outside of the circle.
What is the discontinuity of x2+7x+1/x2+2x-15?
The discontinuity occurs when x is either -5 or 3.
That is determined by solving denominator = 0 quadratic equation for x.
Hope this helps.
The Beer Institute reported that monthly consumption of beer in is 1.7 gallons per person. A random sample of 36 adults was selected. Using a population standard deviation of 0.5 gallons per month per person, what is the probability that the sample mean was between 1.6 and 1.8 gallons per month per person?
Answer:
.7698
Step-by-step explanation:
What is the equation of a circle with center (−8, 3) and radius 8?
Answer:
(x + 8)² + (y - 3)² = 64
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (- 8, 3) and r = 8 , thus
(x - (- 8))² + (y - 3)² = 8² , that is
(x + 8)² + (y - 3)² = 64
Answer:
See below.
Step-by-step explanation:
The equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius.
Plug in what we know. (-8,3) for (h,k) respectively and 8 for the radius:
[tex](x-(-8))^2+(y-(3))^2=(8)^2[/tex]
[tex](x+8)^2+(y-3)^2=64[/tex]
The book was purchased for $8 and half of its price. How much does the book cost?
Answer:
16$
Step-by-step explanation:
8*2=16
HOPE THIS HELPS :)
Answer: $16
Step-by-step explanation:
As the book was purchased for half its price plus 8 you can create the equation 1/2x + 8 = x. Then, simplifying the expression you get x = 16. Thus, the book costs 16 dollars.
Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?
Got the explanation from classmates
N=??? I/Y=5 PV=1000000 PMT=-65000 FV=0
It will last 27 years.
Answer:
27 years
Step-by-step explanation:
The formula for the number of payments can be used:
N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03
There will be a couple thousand dollars left after the 27th payment.
The winnings will last 27 years.
Refer to the accompanying data set and construct a 90​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.
Male/Females
81 82
77 94
53 60
59 66
53 53
60 81
54 78
76 83
52 87
64 53
73 34
57 64
65 83
78 74
79 81
66 66
69 65
94 76
45 61
89 64
71 82
66 80
70 71
74 77
52 88
68 90
56 87
79 91
75 89
62 93
66 68
96 87
60 83
65 81
55 74
57 56
70 101
70 71
83 74
57 77
The required 90% confidence interval for adult males is
[tex]\text {CI} = (64.2, \: 70.6)\\\\[/tex]
The required 90% confidence interval for adult females is
[tex]\text {CI} = (72, \: 79.2)\\\\[/tex]
The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.
Step-by-step explanation:
We are given the pulse rates of adult females and adult males and we have to construct the 90% confidence interval of the mean pulse rate for males and females.
Let us first compute the mean and standard deviation of the given pulse rates data.
Using Excel,
=AVERAGE(number1, number2,....)
The mean pulse rate of adult males is found to be
[tex]\bar{x}_{male} = 67.4[/tex]
The mean pulse rate of adult females is found to be
[tex]\bar{x}_{female} = 75.6[/tex]
Using Excel,
=STDEV(number1, number2,....)
The standard deviation for adult male pulse rate is found to be
[tex]s_{male} = 11.9[/tex]
The standard deviation for adult female pulse rate is found to be
[tex]s_{female} = 13.5[/tex]
The confidence interval is given by
[tex]$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean, n is the sample size, s is the sample standard deviation and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 90% confidence level.
The t-score corresponding to a 90% confidence level is
Significance level = α = 1 - 0.90 = 0.10/2 = 0.05
Degree of freedom = n - 1 = 40 - 1 = 39
From the t-table at α = 0.05 and DoF = 39
t-score = 1.685
The required 90% confidence interval for adult males is
[tex]\text {CI} = 67.4 \pm 1.685\cdot \frac{11.9}{\sqrt{40} } \\\\\text {CI} = 67.4 \pm 1.685\cdot 1.882\\\\\text {CI} = 67.4 \pm 3.17\\\\\text {CI} = 67.4 - 3.17, \: 67.4 + 3.17\\\\\text {CI} = (64.2, \: 70.6)\\\\[/tex]
Therefore, we are 90% confident that the actual mean pulse rate of adult male is within the range of 64.2 to 70.6 bpm
The required 90% confidence interval for adult females is
[tex]\text {CI} = 75.6 \pm 1.685\cdot \frac{13.5}{\sqrt{40} } \\\\\text {CI} = 75.6 \pm 1.685\cdot 2.1345\\\\\text {CI} = 75.6 \pm 3.60\\\\\text {CI} = 75.6 - 3.60, \: 75.6 + 3.60\\\\\text {CI} = (72, \: 79.2)\\\\[/tex]
Therefore, we are 90% confident that the actual mean pulse rate of adult female is within the range of 72 to 79.2 bpm
Comparison:
The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.
Consider circle T with radius 24 in. and θ = StartFraction 5 pi Over 6 EndFraction radians. Circle T is shown. Line segments S T and V T are radii with lengths of 24 inches. Angle S T V is theta. What is the length of minor arc SV?
Answer:
20π inStep-by-step explanation:
Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;
[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]
The length of the minor arc SV is expressed as:
[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]
Hence, The length of the arc SV is 20π in
Answer:
20 pi
Step-by-step explanation:
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 58.2 σ=58.2. You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.
Answer:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Step-by-step explanation:
Let's define some notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=58.2[/tex] represent the population standard deviation
n represent the sample size
[tex] ME =1[/tex] represent the margin of error desire
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Perform the operation 3/a^2+2/ab^2
Answer:
Step-by-step explanation:
Least common denominator = a²b²
[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]
Factor completely 2x3y + 18xy - 10x2y - 90y. I need this done today in a few minutes.
Answer:
2y (x^2+9) ( x-5)
Step-by-step explanation:
2x^3y + 18xy - 10x^2y - 90y
Factor out the common factor of 2y
2y(x^3+9x-5x^2-45)
Then factor by grouping
2y(x^3+9x -5x^2-45)
Taking x from the first group and -5 from the second
2y( x (x^2+9) -5(x^2+9))
Now factor out (x^2+9)
2y (x^2+9) ( x-5)
Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula. [tex]2*sin(x/2)*cos(x/2)[/tex]
Answer:
[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{x}[/tex]
Step-by-step explanation:
The double angle formula states that:
[tex]\sin{2a} = 2\sin{a}\cos{a}[/tex]
In this question:
[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}}[/tex]
So
[tex]a = \frac{x}{2}[/tex]
Then
[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{\frac{2x}{2}} = \sin{x}[/tex]
Among all pairs of numbers whose sum is 6, find a pair whose product is as large as possible. What is the maximum product? The pair of numbers whose sum is 6 and whose product is as large as possible is
Answer:
The pair of numbers is (3,3) while the maximum product is 9
Step-by-step explanation:
The pairs of numbers whose sum is 6 starting from zero is ;
0,6
1,5
2,4
3,3
Kindly note 2,4 is same as 4,2 , so there is no need for repetition
So the maximum product is 3 * 3 = 9 and the pair is 3,3
The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.
Calculation of the pair of the numbers:Since the sum of the pairs is 6
So, here are the following probabilities
0,6
1,5
2,4
3,3
Now if we multiply 3 and 3 so it comes 9 also it should be large
Therefore, The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.
Learn more about numbers here: https://brainly.com/question/13902300
Diagramming Percents
Percents
Total
An item was marked down 60% from its original price.
The amount of the discount was $30. Fill in the
numbers that belong in the diagram to find the original
price
20%
20%
20%
20%
20%
A=
B=
C=
Answer:
see below
Step-by-step explanation:
Let x be the original price
x* discount rate = discount
x * 60% = 30
Change to decimal form
x * .60 = 30
Divide each side by .60
x = 30/.60
x =50
The original price was 50 dollars
Answer:
A-30 B-20 C-50
Step-by-step explanation:
Decide whether the sets are equivalent {d: d is a month of the year} and {g : g is a state in the United States}
Answer:
Non equivalentStep-by-step explanation:
The equivalent between sets is determined by the number of elements. If two sets have the same number of elements, then they are equivalent sets.
In this case, a year has 12 months, and the US has 50 states. So, one month is not equal to 1 state because they have different natures and they represent a different proportion. A month represents 1/12 of a year and a state represents 1/50 of the total number of states.
what is the value of n?
Answer:
the answer is D
Step-by-step explanation:
Answer:
95°
Step-by-step explanation:
To get the value of n° we must get the values of the traingle angle's sides
and to do that :
180°-144°=36° the first one 180°-121°= 59° the second one 180°-(59°+36°)= 85 the third one n) = 180-85° = 95°Which expression is equivalent to -3(2m - 1) - n? 6m - n - 3 6m - n + 3 -6m - n - 3 -6m - n +3
Answer:
-6m+3
Step-by-step explanation:
Answer:
An equivalent value is -6m -n +3
Step-by-step explanation:
Given
-3(2m-1)-n expand
=-6m+3-n
(also equals -6m -n +3 by commutativity)
y-9=-2(x-8) what is the slope?
Answer:
-2Step-by-step explanation:
Write in slope intercept form.
y - 9 = -2(x - 8)
y - 9 = -2x + 16
y = -2x + 16 + 9
y = -2x + 25
y = mx + b
The m is the slope, b is the y-intercept.
y = -2 x + 25
The slope is -2.
The amount of time it takes a bat to eat a frog was recorded for each bat in a random sample of 12 bats. The resulting sample mean and standard deviation were 21.9 minutes and 7.7 minutes, respectively. Assuming it is reasonable to believe that the population distribution of bat mealtimes of frogs is approximately normal, a. Construct a 95% confidence interval for the mean time for a bat to eat a frog. b. Construct a 95% confidence interval for the variance of the time for a bat to eat a frog.
Answer: a. CI for the mean: 17.327 < μ < 26.473
b. CI for variance: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093
Step-by-step explanation:
a. To construct a 95% confidence interval for the mean:
The given data are:
mean = 21.9
s = 7.7
n = 12
df = 12 - 1 = 11
1 - α = 0.05
[tex]\frac{\alpha}{2}[/tex] = 0.025
t-score = [tex]t_{0.025,11}[/tex] = 2.2001
Note: since the sample population is less than 30, it is used a t-score.
The formula for interval:
mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]
Substituing values:
21.9 ± 2.200.[tex]\frac{7.7}{\sqrt{12} }[/tex]
21.9 ± 4.573
The interval is: 17.327 < μ < 26.473
b. A 95% confidence interval for the variance:
The given values are:
[tex]s^{2}[/tex] = [tex]7.7^{2}[/tex]
[tex]s^{2}[/tex] = 59.29
α = 0.05
[tex]\frac{\alpha}{2}[/tex] = 0.025
[tex]1-\frac{\alpha}{2}[/tex] = 0.975
[tex]\chi^{2}_{0.025,11}[/tex] = 21.92
[tex]\chi^{2}_{0.975,11}[/tex] = 3.816
Note: To find the values for [tex]\chi^{2}_{\alpha/2,n-1}[/tex] and [tex]\chi^{2}_{1-\alpha/2,n-1}[/tex], look for them at the chi-square table
The formula to calculate interval:
([tex]\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}}[/tex])
are the lower and upper limits, respectively.
Substituing values:
([tex]\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816}[/tex])
(29.7532, 170.9093)
The interval for variance is: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093
If 2x+9<32 then x could be
Answer:
x < 11.5
Step-by-step explanation:
2x + 9 < 32
(2x + 9) - 9 < 32 - 9
2x < 23
2x/2 < 23/2
x < 11.5
Answer:
x < 11 1/2
Step-by-step explanation:
2x+9<32
Subtract 9 from each side
2x+9-9 < 32-9
2x<23
Divide by 2
2x/2 <23/2
x < 11 1/2
X is any number less than 11 1/2
f(x)=1/3x g(x)= 1/3x f(g(x))= Are they inverses? Please explain.
Answer:
no
Step-by-step explanation:
f(g(x))= x if they are inverses
(x)=1/3x
g(x)= 1/3x
f(g(x)) = 1/3 (g(x) = 1/3 (1/3x) = 1/9x
This is not x so they are not inverse functions
find the LCM and solve, it's very very urgent.
Answers:
1. 10502. 12003. 12004. 33605. 10806. 480please see the attached picture for full solution..
Hope it helps....
Good luck on your assignment...
PLEASE HELP ME!!!!!! Consider what would happen if you were to slice a face at a vertex (cut a corner) of a particular polyhedron. You would see a new polygonal face where the old vertex used to be. What type of polygon would a slice of a cube at a vertex create? Explain how you know.
Answer:
See below.
Step-by-step explanation:
There are 3 edges and 3 faces projecting out from a vertex of a cube.
So the polygon produced would be a triangle.
Answer:
A triangle.
Step-by-step explanation:
As shown above, the plane which slices a corner intersects the polyhedron in [tex] n [/tex] faces which depend on the particular polyhedron.
Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.
Hence the polygon is a triangle.
find the value of k if x minus 2 is a factor of P of X that is X square + X + k
Answer:
k = -6
Step-by-step explanation:
hello
saying that (x-2) is a factor of [tex]x^2+x+k[/tex]
means that 2 is a zero of
[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]
and we can verify as
[tex](x^2+x-6)=(x-2)(x+3)[/tex]
so it is all good
hope this helps
The area of a rectangular horse pasture is 268,500 square yards. The length of the pasture is 5 yards less than three times the width. What is the width of the pasture in yards? Do not include units in your answer. Please help right away! Thank you very much!
Answer: width = 300
Step-by-step explanation:
Area (A) = Length (L) x width (w)
Given: A = 268,500
L = 3w - 5
w = w
268,500 = (3w - 5) x (w)
268,500 = 3w² - 5w
0 = 3w² - 5w - 268,500
0 = (3w + 895) (w - 300)
0 = 3w + 895 0 = w - 300
-985/3 = w 300 = w
Since width cannot be negative, disregard w = -985/3
So the only valid answer is: w = 300
Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that: She rolls a three. (enter the answer as a percent rounded to the nearest tenth as needed)
Answer:
16.7%
Step-by-step explanation:
Each of the six faces of a six-faced die shows one of the numbers: 1, 2, 3, 4, 5, 6.
A roll of a die is equally likely to land on any face, so the total number of possible outputs is 6, corresponding to the number of faces on the die.
The desired outcome here is 3, meaning the face that shows the number 3. Only one face has the number 3, so the number of desired outcomes is 1.
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(3) = 1/6 = 0.16666... = 16.7%
Reese needs to understand the integer laws to complete his homework. As he recites his rules, he is overheard saying "a positive plus a positive is positive, a negative plus a negative is negative, and a positive plus a negative is a negative". Is he right? Explain why or why not?
Answer:
No
Step-by-step explanation:
Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.
To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.
To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.